Przemysław Rola
Schedae Informaticae, Volume 28, 2019, pp. 25 - 47
https://doi.org/10.4467/20838476SI.19.002.14379Independent Component Analysis (ICA) is a method for searching the linear transformation that minimizes the statistical dependence between its components. Most popular ICA methods use kurtosis as a metric of independence (non-Gaussianity) to maximize, such as FastICA and JADE. However, their assumption of fourth-order moment (kurtosis) may not always be satisfied in practice. One of the possible solution is to use third-order moment (skewness) instead of kurtosis, which was applied in ICA_SG and EcoICA. In this paper we present a competitive approach to ICA based on the Split Generalized Gaussian distribution (SGGD), which is well adapted to heavy-tailed as well as asymmetric data. Consequently, we obtain a method which works better than the classical approaches, in both cases: heavy tails and non-symmetric data.
Przemysław Rola
Universitatis Iagellonicae Acta Mathematica, Volume 49, 2011, pp. 59 - 71
https://doi.org/10.4467/20843828AM.12.004.0456We consider the closedness of the modified set of hedgeable claims and new conditions for the absence of arbitrage connected with it in the classical DalangMorton{Willinger Theorem.